Related papers: Annealed averages in spin and matrix models

A longstanding open question in the theory of disordered systems is whether short-range models, such as the random field Ising model or the Edwards-Anderson model, can indeed have the famous properties that characterize mean-field spin…

We develop a real space renormalisation group analysis of disordered models of glasses, in particular of the spin models at the origin of the Random First Order Transition theory. We find three fixed points respectively associated to the…

We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a…

Recent experimental findings on anomalous diffusion have demanded novel models that combine annealed (temporal) and quenched (spatial or static) disorder mechanisms. The comb-model is a simplified description of diffusion on percolation…

We have analyzed a non-randomly frustrated spin model which exhibits behavior remarkably similar to the phenomenology of structural glasses. The high-temperature disordered phase undergoes a strong first-order transition to a long-range…

A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behaviour of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very…

We study maximum entropy mechanisms of information exchange between agents modeled by neural networks and the macroscopic states of a society of such agents in a few situations. Mathematical quantification of surprise, distrust of other…

The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for…

In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…

It has long been known that disorder, perturbing the energy landscape of magnetic systems, can introduce glassy dynamics. However, the controlled role of increasing disorder in driving glass formation remains difficult to isolate in…

The field of disordered systems provides many simple models in which the competing influences of thermal and non-thermal disorder lead to new phases and non-trivial thermal behavior of order parameters. In this paper, we add a model to the…

We report numerical investigation of the glassy behavior of random-field exchange models in three dimensions. Correlation of energy with the magnetization for different numbers of spin components has been studied. There is a profound…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

In this work the diffusion in the quenched trap model with diverging mean waiting times is examined. The approach of randomly stopped time is extensively applied in order to obtain asymptotically exact representation of the disorder…

Spiral spin liquids are correlated states of matter in which a frustrated magnetic system evades order by fluctuating between a set of (nearly) degenerate spin spirals. Here, we investigate the response of spiral spin liquids to quenched…

Modeling complex systems, like neural networks, simple liquids or flocks of birds, often works in reverse to textbook approaches: given data for which averages and correlations are known, we try to find the parameters of a given model…

We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact…

Twisting and stacking two copies of a 2D crystal can produce a long-wavelength periodic interference pattern known as a moir\'e pattern. Performing the same procedure with an aperiodic structure instead generates a single moir\'e spot at…

This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of…

We study Gibbs distributions of spins taking values in a general compact Polish space, interacting via a pair potential along the edges of a generalized random graph with a given asymptotic weight distribution $P$, obtained by annealing…